Coincidentally, Will, I added a new section to the CSB page yesterday on CofG placement. (It will need further amplification in due course.)

Although it is quite simple to derive the CofG position from a set of known or nominated axle weights, for example those plugged into the spreadsheet, I have struggled to derive the converse relationship in the 3-axle case, namely what a set/sets of axle weights would or could be from a nominated CofG position. I thought it should be possible, but I can't isolate the variables in the resolved moment equations, and I think the situation is indeterminate. (In fact I think I have proved it is indeterminate, unless I'm missing something obvious.) I suspect a reverse iterative method could be fruitful, but it's longwinded. The 2-axle case is simple, and the 4-axle case may be partially solvable by symmetry (I haven't tried that yet), but the nasty one is the 3-axle case. Btw, this problem is not specific to CSBs.

It would be useful to give the CofG position on the spreadsheet from the nominated static axle weights*, since it is only the actual implementation of that position in a constructed model that will realise those intended nominated weights. I think we are all aware of the importance of accurate balance - what we don't have a collective handle on yet is the effect(s) of CofG positioning errors. Intuition says that such errors should have slightly less effect on an 8-coupled than on a 6-coupled, but intuition and springs is a dangerous combination, particularly with CSBs. I'll try simulating your O4 leading axle de-loading.

It's a refreshing change to know that at least some people here are interested in this sort of thing.

I'm not particularly enamoured of full-length CSBs for 2-4-0s, but I've been running some simulations on an intentionally de-loaded uncoupled axle. Initial conclusions are that CofG placement and implementation are very critical if porpoising is to be avoided and the coupled axle loads are to remain reasonably equal.

I'd have thought that a true CoG is never going to be found on our models...due to the very nature of it being a model, with a gearbox and motor hanging off 1 of 3 axles. This being the case, weighting the engine so that all downward forces are applied equally across the range of axles is going to be .. difficult. Surely weighting your engine appropriately will give the desired CoG and that looks like a case of 'try untill its right'. I think Will's problem with the O4 has shown that to be true.Or have I misunderstood your posting...would not be the first time

Mike - no I don't think you have misunderstood me at all. On the contrary. The 'CofG' is a theoretical but useful construct, and it is the single point (or axis, for our purposes here, now that we don't need to worry about the lateral instability horrors of compensation) where the total weight of a body (e.g. a complete loco) acts. The CofG axis is determined from a body being in equilibrium, i.e. no rotation, vertically on that axis. The only forces that could produce rotation are the forces between the wheels and the rail. If those wheel forces are chosen (equal or unequal, according to taste), then there will be a CofG axis, which if implemented by a suitable arrangement of weighting in the model, will implement those chosen wheel forces.

Our model difficulty is in implementing and maintaining that chosen CofG axis, and as Will's O4 demonstrates, the importance of trying to get that axis where it should be or needs to be. There are few models where there is space to put "a plug of lead 20 mm long by 12mm in diameter" to balance out some loco crew.

The mindbender for the CSB arena is that, although the CofG will still 'act', all the foregoing is true only for static wheel forces. The CSB game is the error-management business.

Russ Elliott wrote:Although it is quite simple to derive the CofG position from a set of known or nominated axle weights, for example those plugged into the spreadsheet, I have struggled to derive the converse relationship in the 3-axle case, namely what a set/sets of axle weights would or could be from a nominated CofG position. I thought it should be possible, but I can't isolate the variables in the resolved moment equations, and I think the situation is indeterminate. (In fact I think I have proved it is indeterminate, unless I'm missing something obvious.)

I was rather afraid of that but at least I'm pleased that I'm not the only one who couldn't get the maths to work.

Following with some interest the story surrounding CSBs I tried to use the CLAG spreadsheet for my own purposes, predicating a wheel spacing of 28mm + 28 mm and axle loading of 50 gm.After a lot of fiddling I find that spacings to be 17.1, 17.4, 17.4, 17.1. Any slight variation on these throws everything right of kilter, even 0.1 mm.I can see how to do this using a CAD etching, but how on earth would something like an AG frame be measured out, even the High Level fret may not cope?John

John,what are you trying to achieve with these numbers?10-15-15-10 looks to give reasonable results, close to 0.5 mm deflection with the default wire.If this is one of your tenders will you have room for pivots 17mm outside the end axles?

Personally i don't think you should get the supports either side of the centre axle to far from the half way point between axles.Its desirable to have more deflection on the centre axle so you need to bring the end supports inwards until this is achieved. Its nowhere near so critical as you are implying.RegardsKeith

John Bateson wrote:Following with some interest the story surrounding CSBs I tried to use the CLAG spreadsheet for my own purposes, predicating a wheel spacing of 28mm + 28 mm and axle loading of 50 gm.After a lot of fiddling I find that spacings to be 17.1, 17.4, 17.4, 17.1. Any slight variation on these throws everything right of kilter, even 0.1 mm.I can see how to do this using a CAD etching, but how on earth would something like an AG frame be measured out, even the High Level fret may not cope?

John

I don't think there is any point in aiming for an accuracy of better than 0.5mm unless you are absolutely desperate for the very last ounce of adhesion on a driven chassis. After all, if your fulcrum point is a handrail knob which is 1mm wide, the actual point of contact can be more or less anywhere in there.

Part of the problem is the spread sheet and the apparent precision provided by all those decimal places. To use the thing you have to be prepared to accept numbers that are close enough. It will be close enough, and the result work well, without you going for impossibly accurate fulcrum point positions.

There are, in fact, lots of equally valid solutions you can go for. However part of the reason you are struggling is the ones you are playing with are a long way outside the range we would normally bother with. As a solution, it may be hyper sensitive to small changes.

A good rule of thumb is that you would not expect the outer fulcrum point to be very much farther beyond the outer wheels than half the average distance between the wheels, and no closer in than one quarter of that. In your case, the average distance between the wheels is 28mm. Therefore the outer fulcrum point should be somewhere between 1/4 and 1/2 of that beyond the outer wheels. I.e. between 7mm and 14mm.

Once you've chosen an outer fulcrum dimension in that range, it is just a matter of finding the centre one that goes with it. It is possible you might need to nudge the outer fulcrum in or out by 0.5mm to find an acceptable solution for the centre ones which is also in round half milimeters.

When it comes to making the choice of outer fulcrum points, Russ and I differ a little. He likes a longer thicker CSB and hence will be at the 14mm end. I prefer to keep the wire relatively short, as a long wire may not fit within the available body length, so I end going for the 8mm solution and a thinner wire. But you wont catch either of us saying the other solution is wrong.

In any event A Russ like plot would be 13.5, 16.5, 16.5, 13.5 I would go with 8, 14, 14, 8.

The idea is that the centre axles should be slightly softer than the outer two, and the aiming point is 5%. With a symmetrical chassis like this, it is the only variable we really need to worry about. The Russ style plot comes in at 6% while mine goes out to 11%, which is a bit on the soft side but still acceptable unless perhaps you have a big adhesion demand, in which case going for 8.25 would get you back to the optimum point.

Can I suggest you re-read my original posting on this. Link here. It goes through all this in a lot more detail. You may also like to have a go with my version of the spread sheet which is attached to the next post down. This uses exactly the same calculation engine as the GLAG version, but has had a bit more work done on the presentation of the results. It also includes an automatic calculation option, which, being mine, will work out for you the shorter CSB solution that I favour and will rounds the answers to the nearest 0.5mm.

In the unlikely event that some of you might have been finding the posts above hard to follow, and haven't the foggiest idea what the strings of 4 numbers are, I have drawn up the following diagram. This illustrates the four CSB fulcrum plots that we have been discussing. The dimensions are in mm of course.

The wheel base is the same throughout at a symmetrical 28 between the wheels (a Robinson tender John?). The strings of 4 numbers were the fulcrum offsets. i.e the offset of the first fulcrum from the first axle, the 2nd from the middle axle, the 3rd from the middle axle and the 4th from the last axle. That's enough to calculate all remaining dimensions.

In this order down the diagram areJohn's own suggestion 17.1, 17.4, 17.4, 17.1My Russ like suggestion 13.5, 16.5, 16,5, 13.5Keith's suggestion 10, 15, 15, 10 Mine 8, 14, 14, 8 To help you get a good visual impression of the differences between each plot, the horizontal dimensions on these diagrams are very definitely to scale.

csb draw 12 fplot comp.jpg (59.51 KiB) Viewed 10002 times

Its your choice which you favour, but I think Keith's looks the best balanced.

Will, Keith,This is not for a Robinson Tender. They are already on sale and use individual springing a-la-DaveBradwell. The main reason that was done was that the wheels were so close to the frame that there was no space for the usual handrail knob arrangement without moving the frames outwards to a decidedly non-scale position.It is though, an option I am considering for the Robinson locomotives, those with 7' 0" and 7' 3" coupling rods. I had initially planned to use something like the individual springing based on the work pioneered by others, such as shown in the Society Springing System which I have successfully used a few times. These have a 9mm distance either side of the axle centre line for their fixed points.

The main reason I ended up with such a long distance between fixed points is that fitting a hand rail knob to the chassis in the usual way for shorter distances conflicts the area of the footplate supports and the 'exact-scale' spacers (which are very visible in some of the Robinson series). This does mean that the deflection is a little higher than the 0.5mm normally recommended.

It does seem that having a longer distance between fixed points makes the whole thing a lot more sensitive to inaccuracies in fitting these points.

Will L wrote:In the unlikely event that some of you might have been finding the posts above hard to follow, and haven't the foggiest idea what the strings of 4 numbers are, I have drawn up the following diagram. This illustrates the four CSB fulcrum plots that we have been discussing. The dimensions are in mm of course.

Thanks Will, Your diagram makes comparison of the results so much clearer than the numbers alone.

It's true; for locos I have always favoured the promotion of the longer thicker CSB where frame lengths allow. The longer spans minimise errors arising from fulcrum widths, particularly our humble Romford Mr Blobby handrail knob. Any errors using the sensible nearest hole in the 0.5mm increment HL jig will also be minimal.

For tenders, a shorter CSB will be necessary, as typical tender frame lengths will not allow anything else. 3-axle tender wheelbases tend to be symmetrical, and the CLAG page gives a range of readymade solutions for symmetricals, so there's usually no need to go near any spreadsheet.

(The frame length problem area is the 3-axle loco drive bogie.)

As a complement to Will's diagram above, here are the respective spring shapes, to scale (but exaggerated in the vertical direction of course), demonstrating the differences of deflection for the same spring diameter. John's long '17.1' gets a lot a deflection for his diameter, but his outer axle peaks are some way off the beam peak. Keith's '10' and Will's '8' shorter versions are well-centred in that respect, but they won't get nearly as much deflection per diameter. My Russ-like (as Will dubs it) '13.5' is a sort of half-way house.

Chris - you've got it right - fulcrum locations depend on weight distribution rather than finite overall weight, and spring diameter has no affect on fulcrum location.

Since it seems you want to be adventurous and will intentionally put more weight on the leading axle, you should reflect that differential in your input values. Spreadsheet inputs should be wheel weights, not axle weights.

Will L wrote:This is true but we have a problem. We do know that a centre of gravity (CofG) at the centre of the wheel base will give us even distribution of weight across all the wheels and, our spread sheet will deal with it nicely. What we don't have is a good way of calculating what effect moving the CofG away form the centre will have on the wheel loads in a sprung chassis.

This problem arises because the spreadsheet chooses to reverse reality and takes the points of application of load (the fulcrums) as the supports and the supports (the wheels) as the points of application of the load.

If the problem is modelled as it is with the fulcrums applying the load and the wheels as supports them the Weight (the Load) can be distributed quite accurately amongst the fulcrums even with a non-central centre of gravity.

The moments can easily be calculated using Clapeyron's theorem (no need for iteration) and the deflections calculated using the moment area method.

Will L wrote:This is true but we have a problem. We do know that a centre of gravity (CofG) at the centre of the wheel base will give us even distribution of weight across all the wheels and, our spread sheet will deal with it nicely. What we don't have is a good way of calculating what effect moving the CofG away form the centre will have on the wheel loads in a sprung chassis.

This problem arises because the spreadsheet chooses to reverse reality and takes the points of application of load (the fulcrums) as the supports and the supports (the wheels) as the points of application of the load.

Absolutely correct, you clearly understand what you are looking at.

Alan Turner wrote:If the problem is modelled as it is with the fulcrums applying the load and the wheels as supports them the Weight (the Load) can be distributed quite accurately amongst the fulcrums even with a non-central centre of gravity.

The moments can easily be calculated using Clapeyron's theorem (no need for iteration) and the deflections calculated using the moment area method.

Interestingly the very next sentence which you chose not to quote was:-

Will L wrote: (Oh yes please if anybody knows how to do it)

I'm in the position of being able to understand how the spreadsheet works, in as far as I can see how the calculation performs. I'm in no position to confirm or deny the theoretical position, but outcomes strongly suggests it produces valid and useful answers. I don't know enough physics to know if there is a better way of doing it. So I use the tools available to me. If you can provide me with the generalised calculations required I would be happy try them.

DaveyTee wrote:When I first heard about CSBs, I thought that the idea sounded great and that it was the obvious way to go with my next chassis. I have to say, however, that I find the mathematical complexities utterly off-putting and totally beyond me - it seems to me that if a system that I first perceived as relatively simple is in fact this complex, and requires this amount of mathematical knowledge and precision, then it just isn't for me, which is very disappointing. Or is it just being made to seem more difficult than it actually is?

I had the same reaction. I was also put off by remarks about having to re-adjust the balance, plus problems with weight distribution, etc. I am beginning to think this is just too complicated to be practical.

martin goodall wrote:I was also put off by remarks about having to re-adjust the balance, plus problems with weight distribution, etc. I am beginning to think this is just too complicated to be practical.

Weight distribution on a CSB boils down to "you need to have the Centre of Gravity of the loco close to the centre of the wheel base", and the "difficulties with readjusting weight distribution" seem to be what you read into this post that I wrote when I forgot that rule.

I was trying, and apparently failing, to show it was easy to fix once I realised what I had done wrong. The rest was what I hoped would be in interesting post, of the blow by blow kind which I rather like reading from other people, and which admits that the writer may also be learning as he went along.

DaveyTee wrote:....Unfortunately (at least from my point of view) the thread has recently been straying into theoretical aspects that I have found virtually incomprehensible and have left me doubting that I could possibly do the necessary calculations, or ensure sufficient precision (down to 0.5mm, it seems) to achieve success with this method.

Fear not, the method works whether you understand all the esoteric detail or not.

if spread sheets aren't your thing, I'm sure somebody will come up with the numbers for you.

As for the necessary precision. Being able to measure dimensions in units of 0.5mm is about as accurate as you can reasonably expect to get by eye with a decent steel rule. It is good enough to produce models you can feel satisfied with, whatever suspension system you choose. It is achievable, close enough, by anybody who takes sufficient care.

So, while CSB fulcrums do need to be placed with a degree of accuracy, you're careful man with a steel rule should be able to do the job sufficiently well to get a good working result. The HighLevel jig will make it easier, but notice that it too works in units of 0.5mm.

Alan asserts that the load on each axle cannot be the same (second page).I have noted that the rear axles on the 4-6-0 engines on which I am working all seem to have much more solid axle boxes than the front and centre axle boxes. This is the axle under the firebox and presumably does more work. This I feel sure supports Alan's statement.John